Questions: Compound X has a molar mass of 416.41 g/mol and the following composition: element mass % phosphorus 14.88 % chlorine 85.12 % Write the molecular formula of X.

Solution Steps

First, we need to calculate the number of moles of each element in 100 grams of compound \(X\).

• Phosphorus (P):
  \[ \text{Mass of P} = 14.88 \, \text{g} \] The molar mass of phosphorus is approximately \(30.97 \, \text{g/mol}\). \[ \text{Moles of P} = \frac{14.88 \, \text{g}}{30.97 \, \text{g/mol}} = 0.4805 \, \text{mol} \]

• Chlorine (Cl):
  \[ \text{Mass of Cl} = 85.12 \, \text{g} \] The molar mass of chlorine is approximately \(35.45 \, \text{g/mol}\). \[ \text{Moles of Cl} = \frac{85.12 \, \text{g}}{35.45 \, \text{g/mol}} = 2.4017 \, \text{mol} \]

Next, we find the simplest whole number ratio of moles of phosphorus to moles of chlorine.

• Ratio of P to Cl: \[ \text{Ratio} = \frac{0.4805}{0.4805} : \frac{2.4017}{0.4805} = 1 : 5 \]

The empirical formula is based on the simplest whole number ratio of moles of each element. From the ratio calculated, the empirical formula is \( \text{PCl}_5 \).

To find the molecular formula, we compare the molar mass of the empirical formula with the given molar mass of compound \(X\).

• Molar Mass of Empirical Formula \( \text{PCl}_5 \): \[ \text{Molar mass of } \text{PCl}_5 = 30.97 + 5 \times 35.45 = 208.22 \, \text{g/mol} \]

• Molecular Formula: \[ \text{Factor} = \frac{416.41}{208.22} \approx 2 \]

Thus, the molecular formula is \( \text{P}_2\text{Cl}_{10} \).

Final Answer